I am old school, so I like the mohair cinches. To be honest it is mostly because I like the look of them. I also feel they breathe better then the neoprene ones that I have used. However the nice thing about neoprene cinches is the ability to clean them. I used to believe that neoprene cinches would gall a horse faster then mohair, but I no longer believe that. I have a few of both, but when it comes down to it I will pick a mohair cinch over a neoprene.

well, being here in florida kinda leads to different reasons for choices i suppose. Most cinches i have tend to be covered with fleece, so the fleece can be pulled off and washed often, to help avoid fungus in the humidity. I do like the new Airflex thats out, it seems like Neoprene but it's not exactly the same. Easy to clean, with air flow channels. it looks like it has little pillows, lol. also, good for multiple rides in a day so as not to be putting a wet girth back on a horse.

I use nothing but "natural" material on gear. If it is synthetic or man-made, it is not included in my tack. If asked, I will steer people away from it.
I use mohair, exclusively. Alpaca material is becoming available.